Math

A square and an equilateral triangle have equal perimeters. The area of the triangle is
16�ã3 square centimeters, how long in centimeters is a diagonal of the square? Express your answer in simplest radical form.

1. 👍
2. 👎
3. 👁
1. let each side of the square be x cm
let each side of the equilateral triangle be 2y cm (I use 2y to avoid fractions)

so 4x = 6y,
x = 3y/2

using Pythagoras, the height of the triangle is (√3)y
so
(1/2)(2y)(√3)y = 16√3
which solves to y = 4

then x = 3(4)/2 = 6
let the diagonal of the square be d
d^2 = 6^2 + 6^2
d = √72
= 6√2

1. 👍
2. 👎

Similar Questions

1. Math

Can someone please check to see if I answered these true and false statements correctly? Thank you! 1. A triangle can have two right angles. (TRUE??) 2. An equilateral triangle is also an acute. (TRUE??) 3. A right triangle can

2. Algebra 2

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Find the sum of a finite geometric series. The sides of an equilateral triangle measure 16 inches. The midpoints of the

3. Math

A square has an area of 27 square units. If the perimeter of the square is equal to the perimeter of an equilateral triangle, find the area of the equilateral triangle.

4. Math

Classify the triangle by its sides. Triangle has side lengths of 15, 15, and 20. Scalene Triangle. Isosceles Triangle. Equilateral Triangle. Right Triangle.

1. Calculus

An isosceles triangle has a vertex at the origin. Determine the area of the largest such triangle that is bound by the function x^2 + 6y = 48. So, y=8 when x=0 making a vertical side equal to 8. I also determined that there is a

2. Math

Which triangle is NOT possible to construct? Answers: A. A right isosceles triangle B. An acute equilateral triangle C. An Obtuse scalene triangle D. A right equilateral triangle My Answer: C. An Obtuse scalene triangle :)

3. Trig

An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55°. Determine the area of the triangle. Split in half the triangle is a right triangle, so it's three angles are

4. Math, Geometry

A square and an equilateral triangle have equal perimeters. The area of the triangle is 2\sqrt {3} square inches. What is the number of inches in the length of the diagonal of the square? Please give me a full clear explanation

1. Math

A triangle has 2 angles that measure 60 each. Which of the following best describes thiz triangle. A. Right isoseles triangle B. Equilateral triangle C. Obtuse isosceles triangle D. Acute scalene triangle

2. Math

An equilateral triangle and a regular hexagon have equal perimeters. What is the area of the triangle, if the area of the hexagon is 120? I don't get it

3. math

the area of an equilateral triangle is given by the expression s^2 x square root of 3/4, where s is the side length of the triangle. what is the area of the triangle? round to the nearest tenth the triangle is 5 cm on all three

4. MATH

THE RATIO OF THE PERIMETERS OF TWO SIMILAR TRIANGLES IS 1:3. htE AREA OF THE LARGER TRIANGLE IS 27FT^2. WHAT IS THE AREA OF THE SMALLER TRIANGLE. SORRY FOR THE CAPITAL LOCK. MY COMPUTER KEPBOARD WILL NOT PUT IT TO LOWER CASE SORRY